Details

analyze433.0ms (13.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
31.2%	68.6%	0.1%	8
37.4%	59.3%	3.3%	9
45.2%	48.4%	6.4%	10
56.9%	36.7%	6.4%	11
60.5%	30.8%	8.7%	12
64.2%	24.8%	11.1%	13
70.3%	18.6%	11.1%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample965.0ms (29.2%)

Symmetry

(sort y z)

Results

842.0ms	8256×	body	128	valid
58.0ms	588×	body	128	invalid

Compiler

Compiled 32 to 23 computations (28.1% saved)

simplify24.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

419×	`fma-def_binary64`
121×	`fma-neg_binary64`
46×	`distribute-rgt-in_binary64`
45×	`associate-r_binary64`
43×	`associate-l_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	32	10
3	73	10
4	175	10
5	216	10
6	290	10
7	411	10
8	431	10
9	481	10
10	484	10
11	504	10
12	453	10

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

3.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.6b	(.f64 x (-.f64 1 (.f64 y z)))

Compiler

Compiled 30 to 21 computations (30% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (*.f64 y z))
✓	3.4b	(.f64 x (-.f64 1 (.f64 y z)))

series12.0ms (0.4%)

Counts

2 → 42

Calls

2 calls:

9.0ms	(.f64 x (-.f64 1 (.f64 y z)))
3.0ms	(-.f64 1 (*.f64 y z))

rewrite9.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
5×	`distribute-lft-in_binary64`

Counts

2 → 52

Calls

2 calls:

4.0ms	(.f64 x (-.f64 1 (.f64 y z)))
2.0ms	(-.f64 1 (*.f64 y z))

simplify63.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

900×	`fma-def_binary64`
608×	`distribute-neg-out_binary64`
601×	`unsub-neg_binary64`
328×	`associate-l_binary64`
264×	`*-commutative_binary64`

Counts

94 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	1122
1	163	1031
2	520	977
3	1456	950
4	2828	950
5	5227	950

prune66.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	71	7	78
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	71	8	79

Error

0.0b

Counts

79 → 8

Alt Table

Status	Error	Program
✓	3.6b	(.f64 x (-.f64 1 (.f64 y z)))
	40.9b	(cbrt.f64 (pow.f64 (.f64 (-.f64 1 (.f64 y z)) x) 3))
▶	4.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
	4.9b	(-.f64 x (.f64 y (.f64 z x)))
	40.9b	(cbrt.f64 (.f64 (.f64 (.f64 x (-.f64 1 (.f64 y z))) (.f64 x (-.f64 1 (.f64 y z)))) (.f64 x (-.f64 1 (.f64 y z)))))
	14.4b	(.f64 x (.f64 (sqrt.f64 (-.f64 1 (.f64 y z))) (sqrt.f64 (-.f64 1 (.f64 y z)))))
	33.0b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 y z))))
	31.3b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))

Compiler

Compiled 1295 to 660 computations (49% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	1.5b	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z)))
✓	2.1b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))

series212.0ms (6.4%)

Counts

4 → 96

Calls

4 calls:

123.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z)))
36.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
30.0ms	(cbrt.f64 x)
23.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))

rewrite28.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
25×	`distribute-lft-in_binary64`
25×	`distribute-rgt-in_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`

Counts

4 → 137

Calls

4 calls:

9.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
6.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z)))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify124.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

495×	`distribute-rgt-neg-out_binary64`
401×	`fma-def_binary64`
332×	`associate-l_binary64`
321×	`distribute-rgt-in_binary64`
300×	`distribute-lft-in_binary64`

Counts

233 → 198

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	165	2894
1	325	2581
2	1291	2420
3	3232	2351
4	4775	2351
5	4674	2351

prune98.0ms (3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	229	1	230
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	229	9	238

Error

0.0b

Counts

238 → 9

Alt Table

Status	Error	Program
✓	3.6b	(.f64 x (-.f64 1 (.f64 y z)))
	40.9b	(cbrt.f64 (pow.f64 (.f64 (-.f64 1 (.f64 y z)) x) 3))
✓	4.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
▶	4.9b	(-.f64 x (.f64 y (.f64 z x)))
	40.9b	(cbrt.f64 (.f64 (.f64 (.f64 x (-.f64 1 (.f64 y z))) (.f64 x (-.f64 1 (.f64 y z)))) (.f64 x (-.f64 1 (.f64 y z)))))
	14.4b	(.f64 x (.f64 (sqrt.f64 (-.f64 1 (.f64 y z))) (sqrt.f64 (-.f64 1 (.f64 y z)))))
	33.0b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 y z))))
	5.2b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
	31.3b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))

Compiler

Compiled 4931 to 1816 computations (63.2% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (.f64 y (.f64 z x)))
✓	5.9b	(.f64 y (.f64 z x))

series18.0ms (0.6%)

Counts

2 → 18

Calls

2 calls:

11.0ms	(.f64 y (.f64 z x))
8.0ms	(-.f64 x (.f64 y (.f64 z x)))

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

2 → 40

Calls

2 calls:

8.0ms	(.f64 y (.f64 z x))
3.0ms	(-.f64 x (.f64 y (.f64 z x)))

simplify111.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

721×	`fma-def_binary64`
462×	`fma-neg_binary64`
392×	`distribute-rgt-neg-in_binary64`
378×	`distribute-lft-neg-in_binary64`
300×	`distribute-rgt-in_binary64`

Counts

58 → 55

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	682
1	195	637
2	585	609
3	1582	608
4	4260	608
5	4932	608
6	4986	608
7	4996	608
8	4794	608

prune47.0ms (1.4%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	53	2	55
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	53	11	64

Error

0.0b

Counts

64 → 11

Alt Table

Status	Error	Program
✓	3.6b	(.f64 x (-.f64 1 (.f64 y z)))
	40.9b	(cbrt.f64 (pow.f64 (.f64 (-.f64 1 (.f64 y z)) x) 3))
✓	4.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
✓	4.9b	(-.f64 x (.f64 y (.f64 z x)))
	40.9b	(cbrt.f64 (.f64 (.f64 (.f64 x (-.f64 1 (.f64 y z))) (.f64 x (-.f64 1 (.f64 y z)))) (.f64 x (-.f64 1 (.f64 y z)))))
	14.4b	(.f64 x (.f64 (sqrt.f64 (-.f64 1 (.f64 y z))) (sqrt.f64 (-.f64 1 (.f64 y z)))))
	33.0b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 y z))))
	27.8b	(-.f64 x (.f64 (sqrt.f64 (.f64 y (.f64 z x))) (sqrt.f64 (.f64 y (*.f64 z x)))))
	5.3b	(-.f64 x (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x)))))
▶	5.2b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
	31.3b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))

Compiler

Compiled 1103 to 422 computations (61.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 x)
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
	1.5b	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z)))
✓	2.1b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))

series311.0ms (9.4%)

Counts

2 → 48

Calls

2 calls:

287.0ms

(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))

24.0ms

(*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))) (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))) (*.f64 (cbrt.f64 x) (-.f64 1 (*.f64 y z))))

rewrite26.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-exp-log_binary64`
23×	`pow1_binary64`
20×	`distribute-lft-in_binary64`
20×	`distribute-rgt-in_binary64`
15×	`cbrt-unprod_binary64`

Counts

2 → 63

Calls

2 calls:

13.0ms

(*.f64 (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))) (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))) (*.f64 (cbrt.f64 x) (-.f64 1 (*.f64 y z))))

2.0ms

(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))

simplify79.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

490×	`distribute-rgt-neg-out_binary64`
461×	`*-commutative_binary64`
331×	`distribute-rgt-in_binary64`
329×	`associate-l_binary64`
314×	`distribute-lft-in_binary64`

Counts

111 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	2080
1	278	1297
2	1124	1225
3	2918	1189
4	4761	1189

prune123.0ms (3.7%)

Pruning

11 alts after pruning (7 fresh and 4 done)

	Pruned	Kept	Total
New	287	0	287
Fresh	0	7	7
Picked	0	1	1
Done	0	3	3
Total	287	11	298

Error

0.0b

Counts

298 → 11

Alt Table

Status	Error	Program
✓	3.6b	(.f64 x (-.f64 1 (.f64 y z)))
	40.9b	(cbrt.f64 (pow.f64 (.f64 (-.f64 1 (.f64 y z)) x) 3))
✓	4.8b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
✓	4.9b	(-.f64 x (.f64 y (.f64 z x)))
	40.9b	(cbrt.f64 (.f64 (.f64 (.f64 x (-.f64 1 (.f64 y z))) (.f64 x (-.f64 1 (.f64 y z)))) (.f64 x (-.f64 1 (.f64 y z)))))
	14.4b	(.f64 x (.f64 (sqrt.f64 (-.f64 1 (.f64 y z))) (sqrt.f64 (-.f64 1 (.f64 y z)))))
	33.0b	(.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (-.f64 1 (*.f64 y z))))
	27.8b	(-.f64 x (.f64 (sqrt.f64 (.f64 y (.f64 z x))) (sqrt.f64 (.f64 y (*.f64 z x)))))
	5.3b	(-.f64 x (.f64 (.f64 (cbrt.f64 (.f64 y (.f64 z x))) (cbrt.f64 (.f64 y (.f64 z x)))) (cbrt.f64 (.f64 y (.f64 z x)))))
✓	5.2b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 y z))))
	31.3b	(.f64 (sqrt.f64 (.f64 x (-.f64 1 (.f64 y z)))) (sqrt.f64 (.f64 x (-.f64 1 (*.f64 y z)))))

Compiler

Compiled 10401 to 2367 computations (77.2% saved)

regimes385.0ms (11.7%)

Accuracy

Total 0.1b remaining (80%)

Threshold costs 0.1b (80%)

Counts

38 → 3

Compiler

Compiled 5618 to 3311 computations (41.1% saved)

bsearch1.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
7×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`distribute-rgt-neg-in_binary64`
6×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	58
1	35	58
2	54	58
3	65	58
4	72	58
5	74	58
6	73	58

end121.0ms (3.7%)

Remove: (sort y z)
Compiler: Compiled 372 to 201 computations (46% saved)

Iter	Nodes	Cost
0	8	10
1	17	10
2	32	10
3	73	10
4	175	10
5	216	10
6	290	10
7	411	10
8	431	10
9	481	10
10	484	10
11	504	10
12	453	10

Iter	Nodes	Cost
0	8	10
1	17	10
2	32	10
3	73	10
4	175	10
5	216	10
6	290	10
7	411	10
8	431	10
9	481	10
10	484	10
11	504	10
12	453	10

Details

analyze433.0ms (13.1%)

sample965.0ms (29.2%)

simplify24.0ms (0.7%)

prune1.0ms (0%)

localize5.0ms (0.1%)

series12.0ms (0.4%)

rewrite9.0ms (0.3%)

simplify63.0ms (1.9%)

prune66.0ms (2%)

localize8.0ms (0.2%)

series212.0ms (6.4%)

rewrite28.0ms (0.9%)

simplify124.0ms (3.8%)

prune98.0ms (3%)

localize4.0ms (0.1%)

series18.0ms (0.6%)

rewrite12.0ms (0.4%)

simplify111.0ms (3.4%)

prune47.0ms (1.4%)

localize11.0ms (0.3%)

series311.0ms (9.4%)

rewrite26.0ms (0.8%)

simplify79.0ms (2.4%)

prune123.0ms (3.7%)

regimes385.0ms (11.7%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end121.0ms (3.7%)

Profiling

Iter	Nodes	Cost
0	8	10
1	17	10
2	32	10
3	73	10
4	175	10
5	216	10
6	290	10
7	411	10
8	431	10
9	481	10
10	484	10
11	504	10
12	453	10